In this work, a passive reservoir computing scheme is presented, which relies on the excitation and guiding of transverse modes in a large cross-section photonic waveguide. The optical modes act similar to conventional waveguide-based reservoir nodes, whereas random defects act as the operational equivalent of internode connections. Therefore, the proposed scheme's number of nodes and connections can scale with the waveguide's volume, contrary to planar implementations. The principle of operation, alongside the role of mode defects to performance, is validated through a numerical model, whereas the classification of time-dependent, 2D analog/digital image streams is used as an application-relevant benchmark test.